The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  1  1  X  1  X  1  X  1  1 X^2  X  1  X  1  1 X^2  1  1  1  0  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X X^2+X X^2  0  0  0  X X^2+X X^2+X X^2 X^2  0  X  X X^2+X  X  X  X  X X^2  X  X  0  X X^2+X X^2  X  X X^2  X  X X^2  X  X X^2+X  X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2  0 X^2+X X^2+X X^2 X^2+X X^2  X X^2 X^2  X  X  X  0  X X^2  0  X  X X^2+X  X X^2  0 X^2+X X^2+X X^2 X^2+X  X  0  0 X^2+X X^2  0  X X^2 X^2  X  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  0  X X^2+X  X X^2  X  0 X^2+X X^2+X  X X^2  0  X X^2+X X^2 X^2+X X^2  X  0  X  X X^2 X^2+X  0  0  0  0 X^2+X X^2  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+125x^48+4x^49+282x^50+44x^51+386x^52+164x^53+492x^54+300x^55+619x^56+300x^57+468x^58+164x^59+304x^60+44x^61+178x^62+4x^63+128x^64+48x^66+30x^68+2x^70+6x^72+2x^74+1x^88

The gray image is a linear code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 1.06 seconds.